A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

Explanation

To find the area of the traffic signal board, which is in the shape of an equilateral triangle using Heron's formula, we will follow these steps:

### Step 1: Define the sides of the triangle
Since the triangle is equilateral, all three sides are equal. Let the length of each side be denoted as \( a \).

### Step 2: Calculate the semi-perimeter
The semi-perimeter \( s \) of a triangle is given by the formula:
\[
...